Question

The screw of a screw gauge moves $4.5mm$ linearly for every $3$ complete rotations of the ratchet. If the circular scale of the gauge has $95$ divisions, the least count of the screw gauge is:

• A. $0.0158cm$
• B. $0.00158cm$
• C. $1.58\mu m$
• D. $15.8\mu m$

Answer 1

Answer: (B), (D)

$15.8\mu m$

Given: No. of circular scale divisions, $N=95$
The screw moves $4.5mm$ for every 3 rotations of the ratchet or the circular screw head.
$⟹$ The distance moved by the screw for 1 complete rotation of the ratchet, $p=\frac{4.5}{3}=1.5mm$.
$\therefore$The pitch of the screw, $p=1.5mm$
Least count of the screw gauge, $\text{L.C.}=\frac{p}{N}=\frac{1.5}{95}=0.0158mm$
$1mm=0.1cm$
$⟹\text{L.C.}=0.00158cm$
Also $1mm={10}^3\mu m$
$⟹\text{L.C.}=0.0158\times {10}^3=15.8\mu m$.